Results 1 to 2 of 2

Math Help - Linear optimization

  1. #1
    Newbie
    Joined
    Sep 2012
    From
    Maryland
    Posts
    10

    Linear optimization

    A pension fund manager decides to invest a total of at most $39 million in U.S. treasury bonds paying 4%
    annual interest and in mutual funds paying 8% annual interest. He plans to invest at least $5 million in
    bonds and at least $10 million in mutual funds. Bonds have an initial fee of $100 per million dollars,
    while the fee for mutual funds is $200 per million. The fund manager is allowed to spend no more than
    $5000 on fees. How much should be invested in each to maximize annual interest? What is the maximum
    annual interest?

    How would i set up the max and min and then eventually graph it? and thus solve the problem
    Thank you
    Last edited by skeeter; October 1st 2012 at 02:47 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,738
    Thanks
    644

    Re: Trignomy word problem

    Hello, Niaboc!

    I'll set it up . . .


    A pension fund manager decides to invest a total of at most $39 million
    in Treasury Bonds paying 4% annual interest and in Mutual Funds paying 8% annual interest.
    He plans to invest at least $5 million in Trasury Bonds and at least $10 million in Mutual Funds.
    Treasury Bonds have an initial fee of $100 per million dollars, while the fee for Mutual Funds is $200 per million.
    The fund manager is allowed to spend no more than $5000 on fees.

    How much should be invested in each to maximize annual interest?
    What is the maximum annual interest?

    Let x = amount invested in Treasury Bonds (in millions of dollars): x\ge\,0
    Let y = amount invested in Mutual Funds (in millions of dollars): . y \,\ge\,0

    Total invested, $39 million: . x + y \:\le\:39

    Invest at least $10 million in Mutual Funds: . x \,\ge\,10
    Invest at least $5 million in Treasure Bonds: . y \,\ge\,5

    Fee for Treasury Bonds: 100x
    Fee for Mutual Funds: 200y
    Maximum fee, $5000: . 100x + 200y \,\le\,5000

    Maximize interest: . I \:=\:0.04x + 0.08y
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. word problem - the snow plough problem?
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: October 13th 2011, 01:02 PM
  2. Replies: 3
    Last Post: January 2nd 2011, 08:20 PM
  3. 1 Word problem and 1 function problem
    Posted in the Algebra Forum
    Replies: 8
    Last Post: April 21st 2010, 08:01 AM
  4. Replies: 2
    Last Post: January 10th 2009, 05:49 AM

Search Tags


/mathhelpforum @mathhelpforum